Related papers: The geometry in Plato's Meno

Both lectures focus on the first part of the so-called 'mathematical part' of Plato's Theaetetus. In this passage, the young Theaetetus briefly recounts the mathematical lesson given by the geometer Theodorus. The first lecture delves into…

In a previous article, we discussed a paradox in Timaeus' cosmology: that there is no void inside the universe, even though it is entirely filled with polyhedra-a mathematical impossibility (Brisson-Ofman 2025). In the present article, we…

This article provides a historical overview of Geometry of Numbers. 1. Figures, 2. The circuit problem and its relatives, 3. Minkowski lattice point set, 4. The young Hermann Minkowski, 5. The geometry of numbers develops, 6. Minkowski…

In different passages of his dialogues, Plato showed deep mathematically-based physical insights. Regrettably most readers overlooked the respective statements, or they utterly did not understand those hints since they were full of…

In this paper, we study the so-called 'Mathematical part' of Plato's Theaetetus. Its subject concerns the incommensurability of certain magnitudes, in modern terms the question of the rationality or irrationality of the square roots of…

This article is the first part of a study of the so-called 'mathematical part' of Plato's Theaetetus (147d-148b). The subject of this 'mathematical part' is the irrationality, one of the most important topics in early Greek mathematics. As…

This is a study of a problem in geodesy with methods from complex algebraic geometry: for a fixed number of measure points and target points at unknown position in the Euclidean plane, we study the problem of determining their relative…

This article contains a short and entertaining list of unsolved problems in Plane Geometry. Their statement may seem naive and can be understood at an elementary level. But their solutions have refused to appear for forty years in the best…

In a first article (referred here as B-O), we studied the first part of the so-called 'mathematical part' of Plato's Theaetetus, i.e. Theodorus' lesson. In the present one, we consider the sequel and the end of the passage (147d7-148b2), as…

Throughout human history, people have used sight to learn about the world, but only in relatively recent times the science of light has been developed. Egyptians and Mesopotamians made the first known lenses out of quartz, giving birth to…

The nature of the existence, revealed through Human cognitive system, has been evolving since the development of the languages. Part of such revelations were the geometrical forms and the numbers, whose beauty and order, wondrous and…

This article provides a simple geometric interpretation of the quadratic formula. The geometry helps to demystify the formula's complex appearance and casts it into a much simpler existence, thus potentially benefits early algebra students.

The paper reviews the most illustrative cases of the "peculiar/anomalous" experiences of time (and, to a lesser extent, also space) and discusses a simple algebraic geometrical model accounting for the most pronounced of them.

We present, discuss and generalize an elegant geometrical proof of the law of cosines, due to Al Cuoco.

We present two new constructions in the usual euclidean plane. We only deal with 'Grecian Geometry', with this phrase we mean elementary geometry in the two-dimensional space R 2 . We describe and prove two propositions about 'projections'.…

This paper describes the evolution of aspects of differential and algebraic gometry from the mid 17th century till the end of the 18th century.

This article explores the overall geometric manner in which human beings make sense of the world around them by means of their physical theories; in particular, in what are nowadays called pregeometric pictures of Nature. In these, the…

This is a survey of some problems in geometric group theory which I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some…

In this articles we consider very mathematical (if not very plausible) geometric marching. Our marchers will exhibit beautiful mathematics, some familiar and some less so. In a final summary section we discuss the point of all the fancy…

Even though it has been almost a century since quantum mechanics planted roots, the field has its share of unresolved problems. It could be the result of a wrong mathematical structure providing inadequate understanding of the quantum…